LMFDB - Embedded newform 4010.2.a.j.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0200112105$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 16 x^{10} + 30 x^{9} + 93 x^{8} - 162 x^{7} - 238 x^{6} + 391 x^{5} + 240 x^{4} + \cdots - 8 $ x^12 - 2x^11 - 16x^10 + 30x^9 + 93x^8 - 162x^7 - 238x^6 + 391x^5 + 240x^4 - 408x^3 - 42x^2 + 120*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-1.58108$ of defining polynomial
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.58108 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.58108 q^{6} +0.389201 q^{7} +1.00000 q^{8} -0.500177 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.58108 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.58108 q^{6} +0.389201 q^{7} +1.00000 q^{8} -0.500177 q^{9} -1.00000 q^{10} -4.95376 q^{11} +1.58108 q^{12} -1.44502 q^{13} +0.389201 q^{14} -1.58108 q^{15} +1.00000 q^{16} +2.82915 q^{17} -0.500177 q^{18} -1.72826 q^{19} -1.00000 q^{20} +0.615359 q^{21} -4.95376 q^{22} -4.93083 q^{23} +1.58108 q^{24} +1.00000 q^{25} -1.44502 q^{26} -5.53407 q^{27} +0.389201 q^{28} -2.52717 q^{29} -1.58108 q^{30} -7.36296 q^{31} +1.00000 q^{32} -7.83231 q^{33} +2.82915 q^{34} -0.389201 q^{35} -0.500177 q^{36} -7.33567 q^{37} -1.72826 q^{38} -2.28470 q^{39} -1.00000 q^{40} +7.73650 q^{41} +0.615359 q^{42} +1.27856 q^{43} -4.95376 q^{44} +0.500177 q^{45} -4.93083 q^{46} -5.77882 q^{47} +1.58108 q^{48} -6.84852 q^{49} +1.00000 q^{50} +4.47312 q^{51} -1.44502 q^{52} -3.41115 q^{53} -5.53407 q^{54} +4.95376 q^{55} +0.389201 q^{56} -2.73253 q^{57} -2.52717 q^{58} +8.75363 q^{59} -1.58108 q^{60} +1.75098 q^{61} -7.36296 q^{62} -0.194669 q^{63} +1.00000 q^{64} +1.44502 q^{65} -7.83231 q^{66} +12.8073 q^{67} +2.82915 q^{68} -7.79605 q^{69} -0.389201 q^{70} +3.84133 q^{71} -0.500177 q^{72} -3.04269 q^{73} -7.33567 q^{74} +1.58108 q^{75} -1.72826 q^{76} -1.92801 q^{77} -2.28470 q^{78} +2.18643 q^{79} -1.00000 q^{80} -7.24929 q^{81} +7.73650 q^{82} +12.5879 q^{83} +0.615359 q^{84} -2.82915 q^{85} +1.27856 q^{86} -3.99567 q^{87} -4.95376 q^{88} -17.2316 q^{89} +0.500177 q^{90} -0.562403 q^{91} -4.93083 q^{92} -11.6415 q^{93} -5.77882 q^{94} +1.72826 q^{95} +1.58108 q^{96} +3.18700 q^{97} -6.84852 q^{98} +2.47776 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} - 2 q^{3} + 12 q^{4} - 12 q^{5} - 2 q^{6} - 9 q^{7} + 12 q^{8}+O(q^{10}) $ 12 * q + 12 * q^2 - 2 * q^3 + 12 * q^4 - 12 * q^5 - 2 * q^6 - 9 * q^7 + 12 * q^8	\( 12 q + 12 q^{2} - 2 q^{3} + 12 q^{4} - 12 q^{5} - 2 q^{6} - 9 q^{7} + 12 q^{8} - 12 q^{10} + q^{11} - 2 q^{12} - 6 q^{13} - 9 q^{14} + 2 q^{15} + 12 q^{16} - 11 q^{17} - 13 q^{19} - 12 q^{20} - 14 q^{21} + q^{22} - 21 q^{23} - 2 q^{24} + 12 q^{25} - 6 q^{26} - 2 q^{27} - 9 q^{28} - 10 q^{29} + 2 q^{30} - 11 q^{31} + 12 q^{32} - 22 q^{33} - 11 q^{34} + 9 q^{35} - 29 q^{37} - 13 q^{38} - 2 q^{39} - 12 q^{40} - q^{41} - 14 q^{42} - 23 q^{43} + q^{44} - 21 q^{46} - 17 q^{47} - 2 q^{48} - 3 q^{49} + 12 q^{50} - 19 q^{51} - 6 q^{52} - 47 q^{53} - 2 q^{54} - q^{55} - 9 q^{56} - 11 q^{57} - 10 q^{58} + 14 q^{59} + 2 q^{60} - 22 q^{61} - 11 q^{62} - 28 q^{63} + 12 q^{64} + 6 q^{65} - 22 q^{66} - 28 q^{67} - 11 q^{68} - q^{69} + 9 q^{70} - 18 q^{71} - 2 q^{73} - 29 q^{74} - 2 q^{75} - 13 q^{76} - 11 q^{77} - 2 q^{78} - 39 q^{79} - 12 q^{80} - 44 q^{81} - q^{82} - 5 q^{83} - 14 q^{84} + 11 q^{85} - 23 q^{86} - 6 q^{87} + q^{88} - 8 q^{89} - 12 q^{91} - 21 q^{92} - 30 q^{93} - 17 q^{94} + 13 q^{95} - 2 q^{96} - 32 q^{97} - 3 q^{98} - 13 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 - 2 * q^3 + 12 * q^4 - 12 * q^5 - 2 * q^6 - 9 * q^7 + 12 * q^8 - 12 * q^10 + q^11 - 2 * q^12 - 6 * q^13 - 9 * q^14 + 2 * q^15 + 12 * q^16 - 11 * q^17 - 13 * q^19 - 12 * q^20 - 14 * q^21 + q^22 - 21 * q^23 - 2 * q^24 + 12 * q^25 - 6 * q^26 - 2 * q^27 - 9 * q^28 - 10 * q^29 + 2 * q^30 - 11 * q^31 + 12 * q^32 - 22 * q^33 - 11 * q^34 + 9 * q^35 - 29 * q^37 - 13 * q^38 - 2 * q^39 - 12 * q^40 - q^41 - 14 * q^42 - 23 * q^43 + q^44 - 21 * q^46 - 17 * q^47 - 2 * q^48 - 3 * q^49 + 12 * q^50 - 19 * q^51 - 6 * q^52 - 47 * q^53 - 2 * q^54 - q^55 - 9 * q^56 - 11 * q^57 - 10 * q^58 + 14 * q^59 + 2 * q^60 - 22 * q^61 - 11 * q^62 - 28 * q^63 + 12 * q^64 + 6 * q^65 - 22 * q^66 - 28 * q^67 - 11 * q^68 - q^69 + 9 * q^70 - 18 * q^71 - 2 * q^73 - 29 * q^74 - 2 * q^75 - 13 * q^76 - 11 * q^77 - 2 * q^78 - 39 * q^79 - 12 * q^80 - 44 * q^81 - q^82 - 5 * q^83 - 14 * q^84 + 11 * q^85 - 23 * q^86 - 6 * q^87 + q^88 - 8 * q^89 - 12 * q^91 - 21 * q^92 - 30 * q^93 - 17 * q^94 + 13 * q^95 - 2 * q^96 - 32 * q^97 - 3 * q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.58108	0.912839	0.456419	−	0.889765i	$-0.349132\pi$
$3$	1.58108	0.912839	0.456419	+	0.889765i	$0.349132\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.58108	0.645474
$7$	0.389201	0.147104	0.0735520	−	0.997291i	$-0.476567\pi$
$7$	0.389201	0.147104	0.0735520	+	0.997291i	$0.476567\pi$
$8$	1.00000	0.353553
$9$	−0.500177	−0.166726
$10$	−1.00000	−0.316228
$11$	−4.95376	−1.49361	−0.746807	−	0.665040i	$-0.768414\pi$
$11$	−4.95376	−1.49361	−0.746807	+	0.665040i	$0.768414\pi$
$12$	1.58108	0.456419
$13$	−1.44502	−0.400777	−0.200388	−	0.979717i	$-0.564220\pi$
$13$	−1.44502	−0.400777	−0.200388	+	0.979717i	$0.564220\pi$
$14$	0.389201	0.104018
$15$	−1.58108	−0.408234
$16$	1.00000	0.250000
$17$	2.82915	0.686169	0.343085	−	0.939304i	$-0.388528\pi$
$17$	2.82915	0.686169	0.343085	+	0.939304i	$0.388528\pi$
$18$	−0.500177	−0.117893
$19$	−1.72826	−0.396491	−0.198245	−	0.980152i	$-0.563524\pi$
$19$	−1.72826	−0.396491	−0.198245	+	0.980152i	$0.563524\pi$
$20$	−1.00000	−0.223607
$21$	0.615359	0.134282
$22$	−4.95376	−1.05615
$23$	−4.93083	−1.02815	−0.514075	−	0.857745i	$-0.671865\pi$
$23$	−4.93083	−1.02815	−0.514075	+	0.857745i	$0.671865\pi$
$24$	1.58108	0.322737
$25$	1.00000	0.200000
$26$	−1.44502	−0.283392
$27$	−5.53407	−1.06503
$28$	0.389201	0.0735520
$29$	−2.52717	−0.469284	−0.234642	−	0.972082i	$-0.575392\pi$
$29$	−2.52717	−0.469284	−0.234642	+	0.972082i	$0.575392\pi$
$30$	−1.58108	−0.288665
$31$	−7.36296	−1.32243	−0.661214	−	0.750198i	$-0.729958\pi$
$31$	−7.36296	−1.32243	−0.661214	+	0.750198i	$0.729958\pi$
$32$	1.00000	0.176777
$33$	−7.83231	−1.36343
$34$	2.82915	0.485195
$35$	−0.389201	−0.0657869
$36$	−0.500177	−0.0833628
$37$	−7.33567	−1.20598	−0.602989	−	0.797750i	$-0.706024\pi$
$37$	−7.33567	−1.20598	−0.602989	+	0.797750i	$0.706024\pi$
$38$	−1.72826	−0.280361
$39$	−2.28470	−0.365844
$40$	−1.00000	−0.158114
$41$	7.73650	1.20824	0.604119	−	0.796894i	$-0.293525\pi$
$41$	7.73650	1.20824	0.604119	+	0.796894i	$0.293525\pi$
$42$	0.615359	0.0949519
$43$	1.27856	0.194978	0.0974890	−	0.995237i	$-0.468919\pi$
$43$	1.27856	0.194978	0.0974890	+	0.995237i	$0.468919\pi$
$44$	−4.95376	−0.746807
$45$	0.500177	0.0745620
$46$	−4.93083	−0.727011
$47$	−5.77882	−0.842928	−0.421464	−	0.906845i	$-0.638484\pi$
$47$	−5.77882	−0.842928	−0.421464	+	0.906845i	$0.638484\pi$
$48$	1.58108	0.228210
$49$	−6.84852	−0.978360
$50$	1.00000	0.141421
$51$	4.47312	0.626362
$52$	−1.44502	−0.200388
$53$	−3.41115	−0.468558	−0.234279	−	0.972169i	$-0.575273\pi$
$53$	−3.41115	−0.468558	−0.234279	+	0.972169i	$0.575273\pi$
$54$	−5.53407	−0.753092
$55$	4.95376	0.667965
$56$	0.389201	0.0520091
$57$	−2.73253	−0.361932
$58$	−2.52717	−0.331834
$59$	8.75363	1.13963	0.569813	−	0.821775i	$-0.307016\pi$
$59$	8.75363	1.13963	0.569813	+	0.821775i	$0.307016\pi$
$60$	−1.58108	−0.204117
$61$	1.75098	0.224190	0.112095	−	0.993697i	$-0.464244\pi$
$61$	1.75098	0.224190	0.112095	+	0.993697i	$0.464244\pi$
$62$	−7.36296	−0.935097
$63$	−0.194669	−0.0245260
$64$	1.00000	0.125000
$65$	1.44502	0.179233
$66$	−7.83231	−0.964090
$67$	12.8073	1.56466	0.782332	−	0.622861i	$-0.214030\pi$
$67$	12.8073	1.56466	0.782332	+	0.622861i	$0.214030\pi$
$68$	2.82915	0.343085
$69$	−7.79605	−0.938535
$70$	−0.389201	−0.0465184
$71$	3.84133	0.455881	0.227941	−	0.973675i	$-0.426801\pi$
$71$	3.84133	0.455881	0.227941	+	0.973675i	$0.426801\pi$
$72$	−0.500177	−0.0589464
$73$	−3.04269	−0.356120	−0.178060	−	0.984020i	$-0.556982\pi$
$73$	−3.04269	−0.356120	−0.178060	+	0.984020i	$0.556982\pi$
$74$	−7.33567	−0.852755
$75$	1.58108	0.182568
$76$	−1.72826	−0.198245
$77$	−1.92801	−0.219717
$78$	−2.28470	−0.258691
$79$	2.18643	0.245992	0.122996	−	0.992407i	$-0.460750\pi$
$79$	2.18643	0.245992	0.122996	+	0.992407i	$0.460750\pi$
$80$	−1.00000	−0.111803
$81$	−7.24929	−0.805477
$82$	7.73650	0.854354
$83$	12.5879	1.38170	0.690850	−	0.722998i	$-0.257237\pi$
$83$	12.5879	1.38170	0.690850	+	0.722998i	$0.257237\pi$
$84$	0.615359	0.0671411
$85$	−2.82915	−0.306864
$86$	1.27856	0.137870
$87$	−3.99567	−0.428380
$88$	−4.95376	−0.528073
$89$	−17.2316	−1.82655	−0.913274	−	0.407346i	$-0.866454\pi$
$89$	−17.2316	−1.82655	−0.913274	+	0.407346i	$0.866454\pi$
$90$	0.500177	0.0527233
$91$	−0.562403	−0.0589559
$92$	−4.93083	−0.514075
$93$	−11.6415	−1.20716
$94$	−5.77882	−0.596040
$95$	1.72826	0.177316
$96$	1.58108	0.161369
$97$	3.18700	0.323591	0.161795	−	0.986824i	$-0.448272\pi$
$97$	3.18700	0.323591	0.161795	+	0.986824i	$0.448272\pi$
$98$	−6.84852	−0.691805
$99$	2.47776	0.249024
$100$	1.00000	0.100000
$101$	−12.4674	−1.24055	−0.620277	−	0.784383i	$-0.712980\pi$
$101$	−12.4674	−1.24055	−0.620277	+	0.784383i	$0.712980\pi$
$102$	4.47312	0.442905
$103$	1.48104	0.145931	0.0729657	−	0.997334i	$-0.476754\pi$
$103$	1.48104	0.145931	0.0729657	+	0.997334i	$0.476754\pi$
$104$	−1.44502	−0.141696
$105$	−0.615359	−0.0600528
$106$	−3.41115	−0.331320
$107$	−1.40572	−0.135896	−0.0679481	−	0.997689i	$-0.521645\pi$
$107$	−1.40572	−0.135896	−0.0679481	+	0.997689i	$0.521645\pi$
$108$	−5.53407	−0.532516
$109$	−9.35398	−0.895949	−0.447975	−	0.894046i	$-0.647855\pi$
$109$	−9.35398	−0.895949	−0.447975	+	0.894046i	$0.647855\pi$
$110$	4.95376	0.472322
$111$	−11.5983	−1.10086
$112$	0.389201	0.0367760
$113$	0.183008	0.0172160	0.00860799	−	0.999963i	$-0.497260\pi$
$113$	0.183008	0.0172160	0.00860799	+	0.999963i	$0.497260\pi$
$114$	−2.73253	−0.255925
$115$	4.93083	0.459802
$116$	−2.52717	−0.234642
$117$	0.722766	0.0668197
$118$	8.75363	0.805837
$119$	1.10111	0.100938
$120$	−1.58108	−0.144332
$121$	13.5397	1.23089
$122$	1.75098	0.158526
$123$	12.2321	1.10293
$124$	−7.36296	−0.661214
$125$	−1.00000	−0.0894427
$126$	−0.194669	−0.0173425
$127$	−5.96437	−0.529252	−0.264626	−	0.964351i	$-0.585249\pi$
$127$	−5.96437	−0.529252	−0.264626	+	0.964351i	$0.585249\pi$
$128$	1.00000	0.0883883
$129$	2.02150	0.177983
$130$	1.44502	0.126737
$131$	−17.1866	−1.50160	−0.750798	−	0.660532i	$-0.770331\pi$
$131$	−17.1866	−1.50160	−0.750798	+	0.660532i	$0.770331\pi$
$132$	−7.83231	−0.681715
$133$	−0.672641	−0.0583254
$134$	12.8073	1.10639
$135$	5.53407	0.476297
$136$	2.82915	0.242597
$137$	9.17837	0.784161	0.392080	−	0.919931i	$-0.371756\pi$
$137$	9.17837	0.784161	0.392080	+	0.919931i	$0.371756\pi$
$138$	−7.79605	−0.663644
$139$	−1.85376	−0.157234	−0.0786171	−	0.996905i	$-0.525050\pi$
$139$	−1.85376	−0.157234	−0.0786171	+	0.996905i	$0.525050\pi$
$140$	−0.389201	−0.0328935
$141$	−9.13680	−0.769457
$142$	3.84133	0.322357
$143$	7.15829	0.598606
$144$	−0.500177	−0.0416814
$145$	2.52717	0.209870
$146$	−3.04269	−0.251815
$147$	−10.8281	−0.893085
$148$	−7.33567	−0.602989
$149$	−7.88559	−0.646013	−0.323006	−	0.946397i	$-0.604694\pi$
$149$	−7.88559	−0.646013	−0.323006	+	0.946397i	$0.604694\pi$
$150$	1.58108	0.129095
$151$	−8.90485	−0.724667	−0.362333	−	0.932049i	$-0.618020\pi$
$151$	−8.90485	−0.724667	−0.362333	+	0.932049i	$0.618020\pi$
$152$	−1.72826	−0.140181
$153$	−1.41507	−0.114402
$154$	−1.92801	−0.155363
$155$	7.36296	0.591407
$156$	−2.28470	−0.182922
$157$	8.18199	0.652994	0.326497	−	0.945198i	$-0.394132\pi$
$157$	8.18199	0.652994	0.326497	+	0.945198i	$0.394132\pi$
$158$	2.18643	0.173943
$159$	−5.39331	−0.427717
$160$	−1.00000	−0.0790569
$161$	−1.91908	−0.151245
$162$	−7.24929	−0.569558
$163$	−21.3732	−1.67408	−0.837041	−	0.547140i	$-0.815716\pi$
$163$	−21.3732	−1.67408	−0.837041	+	0.547140i	$0.815716\pi$
$164$	7.73650	0.604119
$165$	7.83231	0.609744
$166$	12.5879	0.977009
$167$	4.63680	0.358806	0.179403	−	0.983776i	$-0.442583\pi$
$167$	4.63680	0.358806	0.179403	+	0.983776i	$0.442583\pi$
$168$	0.615359	0.0474759
$169$	−10.9119	−0.839378
$170$	−2.82915	−0.216986
$171$	0.864437	0.0661052
$172$	1.27856	0.0974890
$173$	6.85437	0.521128	0.260564	−	0.965457i	$-0.416091\pi$
$173$	6.85437	0.521128	0.260564	+	0.965457i	$0.416091\pi$
$174$	−3.99567	−0.302911
$175$	0.389201	0.0294208
$176$	−4.95376	−0.373404
$177$	13.8402	1.04029
$178$	−17.2316	−1.29156
$179$	20.4596	1.52923	0.764613	−	0.644490i	$-0.222930\pi$
$179$	20.4596	1.52923	0.764613	+	0.644490i	$0.222930\pi$
$180$	0.500177	0.0372810
$181$	−13.8436	−1.02899	−0.514493	−	0.857495i	$-0.672020\pi$
$181$	−13.8436	−1.02899	−0.514493	+	0.857495i	$0.672020\pi$
$182$	−0.562403	−0.0416881
$183$	2.76844	0.204649
$184$	−4.93083	−0.363506
$185$	7.33567	0.539329
$186$	−11.6415	−0.853593
$187$	−14.0149	−1.02487
$188$	−5.77882	−0.421464
$189$	−2.15386	−0.156671
$190$	1.72826	0.125381
$191$	20.6161	1.49173	0.745864	−	0.666098i	$-0.232037\pi$
$191$	20.6161	1.49173	0.745864	+	0.666098i	$0.232037\pi$
$192$	1.58108	0.114105
$193$	25.9932	1.87103	0.935515	−	0.353288i	$-0.114936\pi$
$193$	25.9932	1.87103	0.935515	+	0.353288i	$0.114936\pi$
$194$	3.18700	0.228813
$195$	2.28470	0.163611
$196$	−6.84852	−0.489180
$197$	24.3313	1.73353	0.866767	−	0.498713i	$-0.166194\pi$
$197$	24.3313	1.73353	0.866767	+	0.498713i	$0.166194\pi$
$198$	2.47776	0.176086
$199$	23.6533	1.67674	0.838368	−	0.545104i	$-0.183510\pi$
$199$	23.6533	1.67674	0.838368	+	0.545104i	$0.183510\pi$
$200$	1.00000	0.0707107
$201$	20.2495	1.42829
$202$	−12.4674	−0.877204
$203$	−0.983576	−0.0690335
$204$	4.47312	0.313181
$205$	−7.73650	−0.540341
$206$	1.48104	0.103189
$207$	2.46629	0.171419
$208$	−1.44502	−0.100194
$209$	8.56141	0.592205
$210$	−0.615359	−0.0424638
$211$	−11.0213	−0.758740	−0.379370	−	0.925245i	$-0.623859\pi$
$211$	−11.0213	−0.758740	−0.379370	+	0.925245i	$0.623859\pi$
$212$	−3.41115	−0.234279
$213$	6.07345	0.416146
$214$	−1.40572	−0.0960931
$215$	−1.27856	−0.0871968
$216$	−5.53407	−0.376546
$217$	−2.86567	−0.194534
$218$	−9.35398	−0.633532
$219$	−4.81075	−0.325080
$220$	4.95376	0.333982
$221$	−4.08818	−0.275001
$222$	−11.5983	−0.778427
$223$	−1.63618	−0.109567	−0.0547833	−	0.998498i	$-0.517447\pi$
$223$	−1.63618	−0.109567	−0.0547833	+	0.998498i	$0.517447\pi$
$224$	0.389201	0.0260046
$225$	−0.500177	−0.0333451
$226$	0.183008	0.0121735
$227$	−7.07318	−0.469463	−0.234732	−	0.972060i	$-0.575421\pi$
$227$	−7.07318	−0.469463	−0.234732	+	0.972060i	$0.575421\pi$
$228$	−2.73253	−0.180966
$229$	9.85543	0.651265	0.325632	−	0.945496i	$-0.394423\pi$
$229$	9.85543	0.651265	0.325632	+	0.945496i	$0.394423\pi$
$230$	4.93083	0.325129
$231$	−3.04834	−0.200566
$232$	−2.52717	−0.165917
$233$	16.8999	1.10715	0.553573	−	0.832800i	$-0.313264\pi$
$233$	16.8999	1.10715	0.553573	+	0.832800i	$0.313264\pi$
$234$	0.722766	0.0472487
$235$	5.77882	0.376969
$236$	8.75363	0.569813
$237$	3.45692	0.224551
$238$	1.10111	0.0713741
$239$	−13.4163	−0.867827	−0.433913	−	0.900955i	$-0.642868\pi$
$239$	−13.4163	−0.867827	−0.433913	+	0.900955i	$0.642868\pi$
$240$	−1.58108	−0.102058
$241$	−22.0776	−1.42214	−0.711071	−	0.703120i	$-0.751790\pi$
$241$	−22.0776	−1.42214	−0.711071	+	0.703120i	$0.751790\pi$
$242$	13.5397	0.870367
$243$	5.14048	0.329762
$244$	1.75098	0.112095
$245$	6.84852	0.437536
$246$	12.2321	0.779887
$247$	2.49738	0.158904
$248$	−7.36296	−0.467549
$249$	19.9025	1.26127
$250$	−1.00000	−0.0632456
$251$	−3.97626	−0.250980	−0.125490	−	0.992095i	$-0.540050\pi$
$251$	−3.97626	−0.250980	−0.125490	+	0.992095i	$0.540050\pi$
$252$	−0.194669	−0.0122630
$253$	24.4262	1.53566
$254$	−5.96437	−0.374238
$255$	−4.47312	−0.280118
$256$	1.00000	0.0625000
$257$	−10.9687	−0.684212	−0.342106	−	0.939661i	$-0.611140\pi$
$257$	−10.9687	−0.684212	−0.342106	+	0.939661i	$0.611140\pi$
$258$	2.02150	0.125853
$259$	−2.85505	−0.177404
$260$	1.44502	0.0896164
$261$	1.26403	0.0782416
$262$	−17.1866	−1.06179
$263$	−15.3051	−0.943755	−0.471877	−	0.881664i	$-0.656423\pi$
$263$	−15.3051	−0.943755	−0.471877	+	0.881664i	$0.656423\pi$
$264$	−7.83231	−0.482045
$265$	3.41115	0.209545
$266$	−0.672641	−0.0412423
$267$	−27.2446	−1.66734
$268$	12.8073	0.782332
$269$	23.9827	1.46225	0.731126	−	0.682243i	$-0.238995\pi$
$269$	23.9827	1.46225	0.731126	+	0.682243i	$0.238995\pi$
$270$	5.53407	0.336793
$271$	−9.17625	−0.557418	−0.278709	−	0.960376i	$-0.589906\pi$
$271$	−9.17625	−0.557418	−0.278709	+	0.960376i	$0.589906\pi$
$272$	2.82915	0.171542
$273$	−0.889206	−0.0538172
$274$	9.17837	0.554485
$275$	−4.95376	−0.298723
$276$	−7.79605	−0.469267
$277$	−0.259149	−0.0155708	−0.00778538	−	0.999970i	$-0.502478\pi$
$277$	−0.259149	−0.0155708	−0.00778538	+	0.999970i	$0.502478\pi$
$278$	−1.85376	−0.111181
$279$	3.68278	0.220482
$280$	−0.389201	−0.0232592
$281$	−9.27764	−0.553458	−0.276729	−	0.960948i	$-0.589250\pi$
$281$	−9.27764	−0.553458	−0.276729	+	0.960948i	$0.589250\pi$
$282$	−9.13680	−0.544088
$283$	9.25627	0.550228	0.275114	−	0.961412i	$-0.411284\pi$
$283$	9.25627	0.550228	0.275114	+	0.961412i	$0.411284\pi$
$284$	3.84133	0.227941
$285$	2.73253	0.161861
$286$	7.15829	0.423278
$287$	3.01105	0.177737
$288$	−0.500177	−0.0294732
$289$	−8.99592	−0.529172
$290$	2.52717	0.148401
$291$	5.03891	0.295386
$292$	−3.04269	−0.178060
$293$	−15.3331	−0.895769	−0.447885	−	0.894091i	$-0.647822\pi$
$293$	−15.3331	−0.895769	−0.447885	+	0.894091i	$0.647822\pi$
$294$	−10.8281	−0.631507
$295$	−8.75363	−0.509656
$296$	−7.33567	−0.426377
$297$	27.4145	1.59075
$298$	−7.88559	−0.456800
$299$	7.12516	0.412058
$300$	1.58108	0.0912839
$301$	0.497615	0.0286820
$302$	−8.90485	−0.512417
$303$	−19.7120	−1.13242
$304$	−1.72826	−0.0991227
$305$	−1.75098	−0.100261
$306$	−1.41507	−0.0808944
$307$	20.8221	1.18838	0.594189	−	0.804326i	$-0.297473\pi$
$307$	20.8221	1.18838	0.594189	+	0.804326i	$0.297473\pi$
$308$	−1.92801	−0.109858
$309$	2.34165	0.133212
$310$	7.36296	0.418188
$311$	3.36099	0.190584	0.0952920	−	0.995449i	$-0.469622\pi$
$311$	3.36099	0.190584	0.0952920	+	0.995449i	$0.469622\pi$
$312$	−2.28470	−0.129346
$313$	−19.4931	−1.10181	−0.550907	−	0.834566i	$-0.685718\pi$
$313$	−19.4931	−1.10181	−0.550907	+	0.834566i	$0.685718\pi$
$314$	8.18199	0.461736
$315$	0.194669	0.0109684
$316$	2.18643	0.122996
$317$	24.9573	1.40174	0.700870	−	0.713289i	$-0.252795\pi$
$317$	24.9573	1.40174	0.700870	+	0.713289i	$0.252795\pi$
$318$	−5.39331	−0.302442
$319$	12.5190	0.700929
$320$	−1.00000	−0.0559017
$321$	−2.22256	−0.124051
$322$	−1.91908	−0.106946
$323$	−4.88952	−0.272060
$324$	−7.24929	−0.402738
$325$	−1.44502	−0.0801553
$326$	−21.3732	−1.18375
$327$	−14.7894	−0.817857
$328$	7.73650	0.427177
$329$	−2.24912	−0.123998
$330$	7.83231	0.431154
$331$	8.07161	0.443656	0.221828	−	0.975086i	$-0.428798\pi$
$331$	8.07161	0.443656	0.221828	+	0.975086i	$0.428798\pi$
$332$	12.5879	0.690850
$333$	3.66913	0.201067
$334$	4.63680	0.253714
$335$	−12.8073	−0.699739
$336$	0.615359	0.0335706
$337$	−31.2449	−1.70202	−0.851009	−	0.525150i	$-0.824009\pi$
$337$	−31.2449	−1.70202	−0.851009	+	0.525150i	$0.824009\pi$
$338$	−10.9119	−0.593530
$339$	0.289351	0.0157154
$340$	−2.82915	−0.153432
$341$	36.4743	1.97520
$342$	0.864437	0.0467434
$343$	−5.38985	−0.291025
$344$	1.27856	0.0689351
$345$	7.79605	0.419725
$346$	6.85437	0.368493
$347$	13.8816	0.745206	0.372603	−	0.927991i	$-0.378465\pi$
$347$	13.8816	0.745206	0.372603	+	0.927991i	$0.378465\pi$
$348$	−3.99567	−0.214190
$349$	−23.7116	−1.26925	−0.634626	−	0.772819i	$-0.718846\pi$
$349$	−23.7116	−1.26925	−0.634626	+	0.772819i	$0.718846\pi$
$350$	0.389201	0.0208037
$351$	7.99685	0.426840
$352$	−4.95376	−0.264036
$353$	−29.1717	−1.55265	−0.776325	−	0.630333i	$-0.782918\pi$
$353$	−29.1717	−1.55265	−0.776325	+	0.630333i	$0.782918\pi$
$354$	13.8402	0.735599
$355$	−3.84133	−0.203876
$356$	−17.2316	−0.913274
$357$	1.74094	0.0921403
$358$	20.4596	1.08133
$359$	−15.8756	−0.837882	−0.418941	−	0.908013i	$-0.637599\pi$
$359$	−15.8756	−0.837882	−0.418941	+	0.908013i	$0.637599\pi$
$360$	0.500177	0.0263616
$361$	−16.0131	−0.842795
$362$	−13.8436	−0.727603
$363$	21.4074	1.12360
$364$	−0.562403	−0.0294779
$365$	3.04269	0.159262
$366$	2.76844	0.144709
$367$	−11.2653	−0.588042	−0.294021	−	0.955799i	$-0.594994\pi$
$367$	−11.2653	−0.588042	−0.294021	+	0.955799i	$0.594994\pi$
$368$	−4.93083	−0.257037
$369$	−3.86962	−0.201444
$370$	7.33567	0.381363
$371$	−1.32762	−0.0689267
$372$	−11.6415	−0.603581
$373$	8.88919	0.460265	0.230132	−	0.973159i	$-0.426084\pi$
$373$	8.88919	0.460265	0.230132	+	0.973159i	$0.426084\pi$
$374$	−14.0149	−0.724694
$375$	−1.58108	−0.0816468
$376$	−5.77882	−0.298020
$377$	3.65181	0.188078
$378$	−2.15386	−0.110783
$379$	16.0885	0.826409	0.413205	−	0.910638i	$-0.364409\pi$
$379$	16.0885	0.826409	0.413205	+	0.910638i	$0.364409\pi$
$380$	1.72826	0.0886581
$381$	−9.43017	−0.483122
$382$	20.6161	1.05481
$383$	−12.7635	−0.652182	−0.326091	−	0.945338i	$-0.605732\pi$
$383$	−12.7635	−0.652182	−0.326091	+	0.945338i	$0.605732\pi$
$384$	1.58108	0.0806843
$385$	1.92801	0.0982603
$386$	25.9932	1.32302
$387$	−0.639504	−0.0325078
$388$	3.18700	0.161795
$389$	20.4901	1.03889	0.519445	−	0.854504i	$-0.326139\pi$
$389$	20.4901	1.03889	0.519445	+	0.854504i	$0.326139\pi$
$390$	2.28470	0.115690
$391$	−13.9501	−0.705485
$392$	−6.84852	−0.345903
$393$	−27.1734	−1.37071
$394$	24.3313	1.22579
$395$	−2.18643	−0.110011
$396$	2.47776	0.124512
$397$	−25.4325	−1.27642	−0.638210	−	0.769863i	$-0.720325\pi$
$397$	−25.4325	−1.27642	−0.638210	+	0.769863i	$0.720325\pi$
$398$	23.6533	1.18563
$399$	−1.06350	−0.0532417
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	20.2495	1.00995
$403$	10.6396	0.529998
$404$	−12.4674	−0.620277
$405$	7.24929	0.360220
$406$	−0.983576	−0.0488141
$407$	36.3392	1.80127
$408$	4.47312	0.221452
$409$	−1.58738	−0.0784910	−0.0392455	−	0.999230i	$-0.512495\pi$
$409$	−1.58738	−0.0784910	−0.0392455	+	0.999230i	$0.512495\pi$
$410$	−7.73650	−0.382079
$411$	14.5118	0.715812
$412$	1.48104	0.0729657
$413$	3.40692	0.167643
$414$	2.46629	0.121211
$415$	−12.5879	−0.617915
$416$	−1.44502	−0.0708480
$417$	−2.93096	−0.143530
$418$	8.56141	0.418752
$419$	12.0122	0.586834	0.293417	−	0.955985i	$-0.405208\pi$
$419$	12.0122	0.586834	0.293417	+	0.955985i	$0.405208\pi$
$420$	−0.615359	−0.0300264
$421$	3.84615	0.187450	0.0937249	−	0.995598i	$-0.470123\pi$
$421$	3.84615	0.187450	0.0937249	+	0.995598i	$0.470123\pi$
$422$	−11.0213	−0.536510
$423$	2.89043	0.140538
$424$	−3.41115	−0.165660
$425$	2.82915	0.137234
$426$	6.07345	0.294260
$427$	0.681482	0.0329792
$428$	−1.40572	−0.0679481
$429$	11.3178	0.546431
$430$	−1.27856	−0.0616574
$431$	−12.7270	−0.613040	−0.306520	−	0.951864i	$-0.599165\pi$
$431$	−12.7270	−0.613040	−0.306520	+	0.951864i	$0.599165\pi$
$432$	−5.53407	−0.266258
$433$	3.18156	0.152896	0.0764480	−	0.997074i	$-0.475642\pi$
$433$	3.18156	0.152896	0.0764480	+	0.997074i	$0.475642\pi$
$434$	−2.86567	−0.137557
$435$	3.99567	0.191577
$436$	−9.35398	−0.447975
$437$	8.52178	0.407652
$438$	−4.81075	−0.229867
$439$	6.38701	0.304835	0.152418	−	0.988316i	$-0.451294\pi$
$439$	6.38701	0.304835	0.152418	+	0.988316i	$0.451294\pi$
$440$	4.95376	0.236161
$441$	3.42547	0.163118
$442$	−4.08818	−0.194455
$443$	−8.45961	−0.401928	−0.200964	−	0.979599i	$-0.564407\pi$
$443$	−8.45961	−0.401928	−0.200964	+	0.979599i	$0.564407\pi$
$444$	−11.5983	−0.550431
$445$	17.2316	0.816857
$446$	−1.63618	−0.0774753
$447$	−12.4678	−0.589705
$448$	0.389201	0.0183880
$449$	35.4001	1.67063	0.835316	−	0.549770i	$-0.185285\pi$
$449$	35.4001	1.67063	0.835316	+	0.549770i	$0.185285\pi$
$450$	−0.500177	−0.0235786
$451$	−38.3248	−1.80464
$452$	0.183008	0.00860799
$453$	−14.0793	−0.661504
$454$	−7.07318	−0.331961
$455$	0.562403	0.0263659
$456$	−2.73253	−0.127962
$457$	−28.2493	−1.32145	−0.660723	−	0.750630i	$-0.729750\pi$
$457$	−28.2493	−1.32145	−0.660723	+	0.750630i	$0.729750\pi$
$458$	9.85543	0.460514
$459$	−15.6567	−0.730792
$460$	4.93083	0.229901
$461$	19.9743	0.930295	0.465148	−	0.885233i	$-0.346001\pi$
$461$	19.9743	0.930295	0.465148	+	0.885233i	$0.346001\pi$
$462$	−3.04834	−0.141822
$463$	−12.0874	−0.561750	−0.280875	−	0.959744i	$-0.590625\pi$
$463$	−12.0874	−0.561750	−0.280875	+	0.959744i	$0.590625\pi$
$464$	−2.52717	−0.117321
$465$	11.6415	0.539859
$466$	16.8999	0.782871
$467$	7.07533	0.327407	0.163704	−	0.986510i	$-0.447656\pi$
$467$	7.07533	0.327407	0.163704	+	0.986510i	$0.447656\pi$
$468$	0.722766	0.0334099
$469$	4.98462	0.230168
$470$	5.77882	0.266557
$471$	12.9364	0.596078
$472$	8.75363	0.402918
$473$	−6.33366	−0.291222
$474$	3.45692	0.158782
$475$	−1.72826	−0.0792982
$476$	1.10111	0.0504691
$477$	1.70618	0.0781205
$478$	−13.4163	−0.613646
$479$	−3.79318	−0.173315	−0.0866575	−	0.996238i	$-0.527619\pi$
$479$	−3.79318	−0.173315	−0.0866575	+	0.996238i	$0.527619\pi$
$480$	−1.58108	−0.0721662
$481$	10.6002	0.483328
$482$	−22.0776	−1.00561
$483$	−3.03423	−0.138062
$484$	13.5397	0.615443
$485$	−3.18700	−0.144714
$486$	5.14048	0.233177
$487$	26.2840	1.19104	0.595522	−	0.803339i	$-0.296945\pi$
$487$	26.2840	1.19104	0.595522	+	0.803339i	$0.296945\pi$
$488$	1.75098	0.0792631
$489$	−33.7929	−1.52817
$490$	6.84852	0.309385
$491$	−1.74390	−0.0787009	−0.0393505	−	0.999225i	$-0.512529\pi$
$491$	−1.74390	−0.0787009	−0.0393505	+	0.999225i	$0.512529\pi$
$492$	12.2321	0.551463
$493$	−7.14974	−0.322008
$494$	2.49738	0.112362
$495$	−2.47776	−0.111367
$496$	−7.36296	−0.330607
$497$	1.49505	0.0670620
$498$	19.9025	0.891852
$499$	35.9854	1.61093	0.805464	−	0.592645i	$-0.201916\pi$
$499$	35.9854	1.61093	0.805464	+	0.592645i	$0.201916\pi$
$500$	−1.00000	−0.0447214
$501$	7.33117	0.327532
$502$	−3.97626	−0.177469
$503$	16.3309	0.728161	0.364080	−	0.931367i	$-0.381383\pi$
$503$	16.3309	0.728161	0.364080	+	0.931367i	$0.381383\pi$
$504$	−0.194669	−0.00867125
$505$	12.4674	0.554792
$506$	24.4262	1.08588
$507$	−17.2526	−0.766217
$508$	−5.96437	−0.264626
$509$	16.3640	0.725323	0.362662	−	0.931921i	$-0.381868\pi$
$509$	16.3640	0.725323	0.362662	+	0.931921i	$0.381868\pi$
$510$	−4.47312	−0.198073
$511$	−1.18422	−0.0523867
$512$	1.00000	0.0441942
$513$	9.56433	0.422276
$514$	−10.9687	−0.483811
$515$	−1.48104	−0.0652625
$516$	2.02150	0.0889917
$517$	28.6269	1.25901
$518$	−2.85505	−0.125444
$519$	10.8373	0.475706
$520$	1.44502	0.0633684
$521$	−4.22836	−0.185248	−0.0926240	−	0.995701i	$-0.529525\pi$
$521$	−4.22836	−0.185248	−0.0926240	+	0.995701i	$0.529525\pi$
$522$	1.26403	0.0553252
$523$	−6.68490	−0.292310	−0.146155	−	0.989262i	$-0.546690\pi$
$523$	−6.68490	−0.292310	−0.146155	+	0.989262i	$0.546690\pi$
$524$	−17.1866	−0.750798
$525$	0.615359	0.0268564
$526$	−15.3051	−0.667335
$527$	−20.8309	−0.907409
$528$	−7.83231	−0.340857
$529$	1.31310	0.0570914
$530$	3.41115	0.148171
$531$	−4.37836	−0.190005
$532$	−0.672641	−0.0291627
$533$	−11.1794	−0.484234
$534$	−27.2446	−1.17899
$535$	1.40572	0.0607746
$536$	12.8073	0.553193
$537$	32.3484	1.39594
$538$	23.9827	1.03397
$539$	33.9259	1.46129
$540$	5.53407	0.238148
$541$	−35.1890	−1.51289	−0.756446	−	0.654056i	$-0.773066\pi$
$541$	−35.1890	−1.51289	−0.756446	+	0.654056i	$0.773066\pi$
$542$	−9.17625	−0.394154
$543$	−21.8879	−0.939298
$544$	2.82915	0.121299
$545$	9.35398	0.400681
$546$	−0.889206	−0.0380545
$547$	19.7773	0.845616	0.422808	−	0.906219i	$-0.361044\pi$
$547$	19.7773	0.845616	0.422808	+	0.906219i	$0.361044\pi$
$548$	9.17837	0.392080
$549$	−0.875799	−0.0373782
$550$	−4.95376	−0.211229
$551$	4.36762	0.186067
$552$	−7.79605	−0.331822
$553$	0.850959	0.0361865
$554$	−0.259149	−0.0110102
$555$	11.5983	0.492321
$556$	−1.85376	−0.0786171
$557$	−17.9344	−0.759907	−0.379953	−	0.925006i	$-0.624060\pi$
$557$	−17.9344	−0.759907	−0.379953	+	0.925006i	$0.624060\pi$
$558$	3.68278	0.155905
$559$	−1.84754	−0.0781426
$560$	−0.389201	−0.0164467
$561$	−22.1588	−0.935543
$562$	−9.27764	−0.391354
$563$	−35.5660	−1.49893	−0.749465	−	0.662044i	$-0.769689\pi$
$563$	−35.5660	−1.49893	−0.749465	+	0.662044i	$0.769689\pi$
$564$	−9.13680	−0.384729
$565$	−0.183008	−0.00769922
$566$	9.25627	0.389070
$567$	−2.82143	−0.118489
$568$	3.84133	0.161178
$569$	32.4368	1.35982	0.679911	−	0.733295i	$-0.262018\pi$
$569$	32.4368	1.35982	0.679911	+	0.733295i	$0.262018\pi$
$570$	2.73253	0.114453
$571$	3.50548	0.146700	0.0733499	−	0.997306i	$-0.476631\pi$
$571$	3.50548	0.146700	0.0733499	+	0.997306i	$0.476631\pi$
$572$	7.15829	0.299303
$573$	32.5958	1.36171
$574$	3.01105	0.125679
$575$	−4.93083	−0.205630
$576$	−0.500177	−0.0208407
$577$	36.9882	1.53984	0.769919	−	0.638142i	$-0.220297\pi$
$577$	36.9882	1.53984	0.769919	+	0.638142i	$0.220297\pi$
$578$	−8.99592	−0.374181
$579$	41.0974	1.70795
$580$	2.52717	0.104935
$581$	4.89921	0.203254
$582$	5.03891	0.208870
$583$	16.8980	0.699845
$584$	−3.04269	−0.125908
$585$	−0.722766	−0.0298827
$586$	−15.3331	−0.633404
$587$	0.365289	0.0150771	0.00753854	−	0.999972i	$-0.497600\pi$
$587$	0.365289	0.0150771	0.00753854	+	0.999972i	$0.497600\pi$
$588$	−10.8281	−0.446543
$589$	12.7251	0.524330
$590$	−8.75363	−0.360381
$591$	38.4698	1.58244
$592$	−7.33567	−0.301494
$593$	−11.3295	−0.465246	−0.232623	−	0.972567i	$-0.574731\pi$
$593$	−11.3295	−0.465246	−0.232623	+	0.972567i	$0.574731\pi$
$594$	27.4145	1.12483
$595$	−1.10111	−0.0451410
$596$	−7.88559	−0.323006
$597$	37.3978	1.53059
$598$	7.12516	0.291369
$599$	4.37941	0.178938	0.0894690	−	0.995990i	$-0.471483\pi$
$599$	4.37941	0.178938	0.0894690	+	0.995990i	$0.471483\pi$
$600$	1.58108	0.0645474
$601$	5.02536	0.204989	0.102494	−	0.994734i	$-0.467318\pi$
$601$	5.02536	0.204989	0.102494	+	0.994734i	$0.467318\pi$
$602$	0.497615	0.0202813
$603$	−6.40593	−0.260870
$604$	−8.90485	−0.362333
$605$	−13.5397	−0.550469
$606$	−19.7120	−0.800745
$607$	−9.14111	−0.371026	−0.185513	−	0.982642i	$-0.559395\pi$
$607$	−9.14111	−0.371026	−0.185513	+	0.982642i	$0.559395\pi$
$608$	−1.72826	−0.0700904
$609$	−1.55512	−0.0630165
$610$	−1.75098	−0.0708951
$611$	8.35052	0.337826
$612$	−1.41507	−0.0572010
$613$	−18.3643	−0.741728	−0.370864	−	0.928687i	$-0.620938\pi$
$613$	−18.3643	−0.741728	−0.370864	+	0.928687i	$0.620938\pi$
$614$	20.8221	0.840310
$615$	−12.2321	−0.493244
$616$	−1.92801	−0.0776816
$617$	33.6430	1.35442	0.677209	−	0.735791i	$-0.263189\pi$
$617$	33.6430	1.35442	0.677209	+	0.735791i	$0.263189\pi$
$618$	2.34165	0.0941950
$619$	41.7967	1.67995	0.839976	−	0.542623i	$-0.182569\pi$
$619$	41.7967	1.67995	0.839976	+	0.542623i	$0.182569\pi$
$620$	7.36296	0.295704
$621$	27.2876	1.09501
$622$	3.36099	0.134763
$623$	−6.70656	−0.268693
$624$	−2.28470	−0.0914611
$625$	1.00000	0.0400000
$626$	−19.4931	−0.779101
$627$	13.5363	0.540587
$628$	8.18199	0.326497
$629$	−20.7537	−0.827504
$630$	0.194669	0.00775580
$631$	−11.4940	−0.457569	−0.228785	−	0.973477i	$-0.573475\pi$
$631$	−11.4940	−0.457569	−0.228785	+	0.973477i	$0.573475\pi$
$632$	2.18643	0.0869715
$633$	−17.4256	−0.692607
$634$	24.9573	0.991180
$635$	5.96437	0.236689
$636$	−5.39331	−0.213859
$637$	9.89626	0.392104
$638$	12.5190	0.495632
$639$	−1.92134	−0.0760071
$640$	−1.00000	−0.0395285
$641$	26.7400	1.05617	0.528083	−	0.849193i	$-0.322911\pi$
$641$	26.7400	1.05617	0.528083	+	0.849193i	$0.322911\pi$
$642$	−2.22256	−0.0877175
$643$	11.2472	0.443547	0.221774	−	0.975098i	$-0.428815\pi$
$643$	11.2472	0.443547	0.221774	+	0.975098i	$0.428815\pi$
$644$	−1.91908	−0.0756225
$645$	−2.02150	−0.0795966
$646$	−4.88952	−0.192375
$647$	−21.9269	−0.862034	−0.431017	−	0.902344i	$-0.641845\pi$
$647$	−21.9269	−0.862034	−0.431017	+	0.902344i	$0.641845\pi$
$648$	−7.24929	−0.284779
$649$	−43.3634	−1.70216
$650$	−1.44502	−0.0566784
$651$	−4.53086	−0.177578
$652$	−21.3732	−0.837041
$653$	−24.8271	−0.971559	−0.485779	−	0.874081i	$-0.661464\pi$
$653$	−24.8271	−0.971559	−0.485779	+	0.874081i	$0.661464\pi$
$654$	−14.7894	−0.578312
$655$	17.1866	0.671534
$656$	7.73650	0.302060
$657$	1.52188	0.0593744
$658$	−2.24912	−0.0876799
$659$	−17.4945	−0.681491	−0.340745	−	0.940156i	$-0.610679\pi$
$659$	−17.4945	−0.681491	−0.340745	+	0.940156i	$0.610679\pi$
$660$	7.83231	0.304872
$661$	−37.2550	−1.44905	−0.724526	−	0.689247i	$-0.757941\pi$
$661$	−37.2550	−1.44905	−0.724526	+	0.689247i	$0.757941\pi$
$662$	8.07161	0.313712
$663$	−6.46375	−0.251031
$664$	12.5879	0.488505
$665$	0.672641	0.0260839
$666$	3.66913	0.142176
$667$	12.4611	0.482494
$668$	4.63680	0.179403
$669$	−2.58693	−0.100017
$670$	−12.8073	−0.494790
$671$	−8.67393	−0.334853
$672$	0.615359	0.0237380
$673$	−25.9937	−1.00198	−0.500992	−	0.865452i	$-0.667031\pi$
$673$	−25.9937	−1.00198	−0.500992	+	0.865452i	$0.667031\pi$
$674$	−31.2449	−1.20351
$675$	−5.53407	−0.213006
$676$	−10.9119	−0.419689
$677$	18.6629	0.717273	0.358637	−	0.933477i	$-0.383242\pi$
$677$	18.6629	0.717273	0.358637	+	0.933477i	$0.383242\pi$
$678$	0.289351	0.0111125
$679$	1.24038	0.0476015
$680$	−2.82915	−0.108493
$681$	−11.1833	−0.428544
$682$	36.4743	1.39667
$683$	−17.8549	−0.683197	−0.341599	−	0.939846i	$-0.610968\pi$
$683$	−17.8549	−0.683197	−0.341599	+	0.939846i	$0.610968\pi$
$684$	0.864437	0.0330526
$685$	−9.17837	−0.350687
$686$	−5.38985	−0.205786
$687$	15.5822	0.594500
$688$	1.27856	0.0487445
$689$	4.92918	0.187787
$690$	7.79605	0.296791
$691$	−18.9350	−0.720323	−0.360161	−	0.932890i	$-0.617278\pi$
$691$	−18.9350	−0.720323	−0.360161	+	0.932890i	$0.617278\pi$
$692$	6.85437	0.260564
$693$	0.964344	0.0366324
$694$	13.8816	0.526940
$695$	1.85376	0.0703173
$696$	−3.99567	−0.151455
$697$	21.8877	0.829056
$698$	−23.7116	−0.897497
$699$	26.7201	1.01065
$700$	0.389201	0.0147104
$701$	7.52403	0.284179	0.142089	−	0.989854i	$-0.454618\pi$
$701$	7.52403	0.284179	0.142089	+	0.989854i	$0.454618\pi$
$702$	7.99685	0.301822
$703$	12.6780	0.478159
$704$	−4.95376	−0.186702
$705$	9.13680	0.344112
$706$	−29.1717	−1.09789
$707$	−4.85232	−0.182490
$708$	13.8402	0.520147
$709$	−45.2206	−1.69830	−0.849148	−	0.528155i	$-0.822884\pi$
$709$	−45.2206	−1.69830	−0.849148	+	0.528155i	$0.822884\pi$
$710$	−3.84133	−0.144162
$711$	−1.09360	−0.0410132
$712$	−17.2316	−0.645782
$713$	36.3055	1.35965
$714$	1.74094	0.0651531
$715$	−7.15829	−0.267705
$716$	20.4596	0.764613
$717$	−21.2122	−0.792186
$718$	−15.8756	−0.592472
$719$	9.45175	0.352491	0.176245	−	0.984346i	$-0.443605\pi$
$719$	9.45175	0.352491	0.176245	+	0.984346i	$0.443605\pi$
$720$	0.500177	0.0186405
$721$	0.576423	0.0214671
$722$	−16.0131	−0.595946
$723$	−34.9065	−1.29819
$724$	−13.8436	−0.514493
$725$	−2.52717	−0.0938567
$726$	21.4074	0.794505
$727$	20.1380	0.746878	0.373439	−	0.927655i	$-0.378178\pi$
$727$	20.1380	0.746878	0.373439	+	0.927655i	$0.378178\pi$
$728$	−0.562403	−0.0208440
$729$	29.8754	1.10650
$730$	3.04269	0.112615
$731$	3.61722	0.133788
$732$	2.76844	0.102325
$733$	−6.88582	−0.254333	−0.127167	−	0.991881i	$-0.540588\pi$
$733$	−6.88582	−0.254333	−0.127167	+	0.991881i	$0.540588\pi$
$734$	−11.2653	−0.415809
$735$	10.8281	0.399400
$736$	−4.93083	−0.181753
$737$	−63.4445	−2.33701
$738$	−3.86962	−0.142443
$739$	−1.89567	−0.0697333	−0.0348666	−	0.999392i	$-0.511101\pi$
$739$	−1.89567	−0.0697333	−0.0348666	+	0.999392i	$0.511101\pi$
$740$	7.33567	0.269665
$741$	3.94856	0.145054
$742$	−1.32762	−0.0487385
$743$	−5.92305	−0.217296	−0.108648	−	0.994080i	$-0.534652\pi$
$743$	−5.92305	−0.217296	−0.108648	+	0.994080i	$0.534652\pi$
$744$	−11.6415	−0.426796
$745$	7.88559	0.288906
$746$	8.88919	0.325456
$747$	−6.29617	−0.230365
$748$	−14.0149	−0.512436
$749$	−0.547107	−0.0199909
$750$	−1.58108	−0.0577330
$751$	−46.0355	−1.67986	−0.839930	−	0.542694i	$-0.817404\pi$
$751$	−46.0355	−1.67986	−0.839930	+	0.542694i	$0.817404\pi$
$752$	−5.77882	−0.210732
$753$	−6.28680	−0.229104
$754$	3.65181	0.132991
$755$	8.90485	0.324081
$756$	−2.15386	−0.0783353
$757$	−9.71004	−0.352918	−0.176459	−	0.984308i	$-0.556464\pi$
$757$	−9.71004	−0.352918	−0.176459	+	0.984308i	$0.556464\pi$
$758$	16.0885	0.584359
$759$	38.6198	1.40181
$760$	1.72826	0.0626907
$761$	14.2189	0.515434	0.257717	−	0.966220i	$-0.417030\pi$
$761$	14.2189	0.515434	0.257717	+	0.966220i	$0.417030\pi$
$762$	−9.43017	−0.341619
$763$	−3.64058	−0.131798
$764$	20.6161	0.745864
$765$	1.41507	0.0511621
$766$	−12.7635	−0.461162
$767$	−12.6492	−0.456735
$768$	1.58108	0.0570524
$769$	−41.0670	−1.48091	−0.740457	−	0.672104i	$-0.765391\pi$
$769$	−41.0670	−1.48091	−0.740457	+	0.672104i	$0.765391\pi$
$770$	1.92801	0.0694805
$771$	−17.3425	−0.624575
$772$	25.9932	0.935515
$773$	−1.64874	−0.0593009	−0.0296505	−	0.999560i	$-0.509439\pi$
$773$	−1.64874	−0.0593009	−0.0296505	+	0.999560i	$0.509439\pi$
$774$	−0.639504	−0.0229865
$775$	−7.36296	−0.264485
$776$	3.18700	0.114407
$777$	−4.51407	−0.161941
$778$	20.4901	0.734606
$779$	−13.3707	−0.479056
$780$	2.28470	0.0818053
$781$	−19.0290	−0.680911
$782$	−13.9501	−0.498853
$783$	13.9855	0.499802
$784$	−6.84852	−0.244590
$785$	−8.18199	−0.292028
$786$	−27.1734	−0.969242
$787$	−16.1753	−0.576586	−0.288293	−	0.957542i	$-0.593088\pi$
$787$	−16.1753	−0.576586	−0.288293	+	0.957542i	$0.593088\pi$
$788$	24.3313	0.866767
$789$	−24.1987	−0.861496
$790$	−2.18643	−0.0777896
$791$	0.0712270	0.00253254
$792$	2.47776	0.0880432
$793$	−2.53020	−0.0898501
$794$	−25.4325	−0.902565
$795$	5.39331	0.191281
$796$	23.6533	0.838368
$797$	−9.80225	−0.347214	−0.173607	−	0.984815i	$-0.555542\pi$
$797$	−9.80225	−0.347214	−0.173607	+	0.984815i	$0.555542\pi$
$798$	−1.06350	−0.0376476
$799$	−16.3491	−0.578391
$800$	1.00000	0.0353553
$801$	8.61885	0.304532
$802$	1.00000	0.0353112
$803$	15.0728	0.531907
$804$	20.2495	0.714143
$805$	1.91908	0.0676388
$806$	10.6396	0.374765
$807$	37.9186	1.33480
$808$	−12.4674	−0.438602
$809$	−38.7474	−1.36229	−0.681144	−	0.732150i	$-0.738517\pi$
$809$	−38.7474	−1.36229	−0.681144	+	0.732150i	$0.738517\pi$
$810$	7.24929	0.254714
$811$	−17.3131	−0.607946	−0.303973	−	0.952681i	$-0.598313\pi$
$811$	−17.3131	−0.607946	−0.303973	+	0.952681i	$0.598313\pi$
$812$	−0.983576	−0.0345168
$813$	−14.5084	−0.508832
$814$	36.3392	1.27369
$815$	21.3732	0.748672
$816$	4.47312	0.156590
$817$	−2.20968	−0.0773070
$818$	−1.58738	−0.0555016
$819$	0.281301	0.00982945
$820$	−7.73650	−0.270170
$821$	−7.27907	−0.254041	−0.127021	−	0.991900i	$-0.540541\pi$
$821$	−7.27907	−0.254041	−0.127021	+	0.991900i	$0.540541\pi$
$822$	14.5118	0.506156
$823$	3.97560	0.138581	0.0692904	−	0.997597i	$-0.477927\pi$
$823$	3.97560	0.138581	0.0692904	+	0.997597i	$0.477927\pi$
$824$	1.48104	0.0515946
$825$	−7.83231	−0.272686
$826$	3.40692	0.118542
$827$	47.7266	1.65962	0.829809	−	0.558048i	$-0.188449\pi$
$827$	47.7266	1.65962	0.829809	+	0.558048i	$0.188449\pi$
$828$	2.46629	0.0857094
$829$	16.5935	0.576315	0.288158	−	0.957583i	$-0.406957\pi$
$829$	16.5935	0.576315	0.288158	+	0.957583i	$0.406957\pi$
$830$	−12.5879	−0.436932
$831$	−0.409736	−0.0142136
$832$	−1.44502	−0.0500971
$833$	−19.3755	−0.671321
$834$	−2.93096	−0.101491
$835$	−4.63680	−0.160463
$836$	8.56141	0.296102
$837$	40.7471	1.40843
$838$	12.0122	0.414954
$839$	−4.53401	−0.156532	−0.0782658	−	0.996933i	$-0.524938\pi$
$839$	−4.53401	−0.156532	−0.0782658	+	0.996933i	$0.524938\pi$
$840$	−0.615359	−0.0212319
$841$	−22.6134	−0.779773
$842$	3.84615	0.132547
$843$	−14.6687	−0.505218
$844$	−11.0213	−0.379370
$845$	10.9119	0.375381
$846$	2.89043	0.0993751
$847$	5.26968	0.181068
$848$	−3.41115	−0.117139
$849$	14.6349	0.502269
$850$	2.82915	0.0970390
$851$	36.1710	1.23992
$852$	6.07345	0.208073
$853$	55.4142	1.89735	0.948673	−	0.316257i	$-0.102426\pi$
$853$	55.4142	1.89735	0.948673	+	0.316257i	$0.102426\pi$
$854$	0.681482	0.0233198
$855$	−0.864437	−0.0295631
$856$	−1.40572	−0.0480465
$857$	−32.8169	−1.12100	−0.560502	−	0.828153i	$-0.689392\pi$
$857$	−32.8169	−1.12100	−0.560502	+	0.828153i	$0.689392\pi$
$858$	11.3178	0.386385
$859$	−1.84754	−0.0630372	−0.0315186	−	0.999503i	$-0.510034\pi$
$859$	−1.84754	−0.0630372	−0.0315186	+	0.999503i	$0.510034\pi$
$860$	−1.27856	−0.0435984
$861$	4.76072	0.162245
$862$	−12.7270	−0.433485
$863$	−44.6047	−1.51836	−0.759180	−	0.650880i	$-0.774400\pi$
$863$	−44.6047	−1.51836	−0.759180	+	0.650880i	$0.774400\pi$
$864$	−5.53407	−0.188273
$865$	−6.85437	−0.233056
$866$	3.18156	0.108114
$867$	−14.2233	−0.483048
$868$	−2.86567	−0.0972672
$869$	−10.8310	−0.367418
$870$	3.99567	0.135466
$871$	−18.5069	−0.627081
$872$	−9.35398	−0.316766
$873$	−1.59406	−0.0539509
$874$	8.52178	0.288253
$875$	−0.389201	−0.0131574
$876$	−4.81075	−0.162540
$877$	27.3962	0.925103	0.462552	−	0.886592i	$-0.346934\pi$
$877$	27.3962	0.925103	0.462552	+	0.886592i	$0.346934\pi$
$878$	6.38701	0.215551
$879$	−24.2429	−0.817693
$880$	4.95376	0.166991
$881$	2.88660	0.0972521	0.0486261	−	0.998817i	$-0.484516\pi$
$881$	2.88660	0.0972521	0.0486261	+	0.998817i	$0.484516\pi$
$882$	3.42547	0.115342
$883$	−9.78908	−0.329429	−0.164714	−	0.986341i	$-0.552670\pi$
$883$	−9.78908	−0.329429	−0.164714	+	0.986341i	$0.552670\pi$
$884$	−4.08818	−0.137500
$885$	−13.8402	−0.465234
$886$	−8.45961	−0.284206
$887$	10.4066	0.349419	0.174710	−	0.984620i	$-0.444101\pi$
$887$	10.4066	0.349419	0.174710	+	0.984620i	$0.444101\pi$
$888$	−11.5983	−0.389214
$889$	−2.32134	−0.0778552
$890$	17.2316	0.577605
$891$	35.9113	1.20307
$892$	−1.63618	−0.0547833
$893$	9.98733	0.334213
$894$	−12.4678	−0.416985
$895$	−20.4596	−0.683890
$896$	0.389201	0.0130023
$897$	11.2655	0.376143
$898$	35.4001	1.18132
$899$	18.6075	0.620593
$900$	−0.500177	−0.0166726
$901$	−9.65065	−0.321510
$902$	−38.3248	−1.27608
$903$	0.786770	0.0261821
$904$	0.183008	0.00608677
$905$	13.8436	0.460176
$906$	−14.0793	−0.467754
$907$	43.4277	1.44199	0.720997	−	0.692938i	$-0.243684\pi$
$907$	43.4277	1.44199	0.720997	+	0.692938i	$0.243684\pi$
$908$	−7.07318	−0.234732
$909$	6.23591	0.206832
$910$	0.562403	0.0186435
$911$	13.2833	0.440096	0.220048	−	0.975489i	$-0.429379\pi$
$911$	13.2833	0.440096	0.220048	+	0.975489i	$0.429379\pi$
$912$	−2.73253	−0.0904831
$913$	−62.3574	−2.06373
$914$	−28.2493	−0.934404
$915$	−2.76844	−0.0915219
$916$	9.85543	0.325632
$917$	−6.68902	−0.220891
$918$	−15.6567	−0.516748
$919$	−32.2193	−1.06282	−0.531408	−	0.847116i	$-0.678337\pi$
$919$	−32.2193	−1.06282	−0.531408	+	0.847116i	$0.678337\pi$
$920$	4.93083	0.162565
$921$	32.9214	1.08480
$922$	19.9743	0.657818
$923$	−5.55080	−0.182707
$924$	−3.04834	−0.100283
$925$	−7.33567	−0.241195
$926$	−12.0874	−0.397217
$927$	−0.740783	−0.0243305
$928$	−2.52717	−0.0829584
$929$	−19.2552	−0.631742	−0.315871	−	0.948802i	$-0.602297\pi$
$929$	−19.2552	−0.631742	−0.315871	+	0.948802i	$0.602297\pi$
$930$	11.6415	0.381738
$931$	11.8361	0.387911
$932$	16.8999	0.553573
$933$	5.31400	0.173973
$934$	7.07533	0.231512
$935$	14.0149	0.458337
$936$	0.722766	0.0236243
$937$	31.7320	1.03664	0.518320	−	0.855187i	$-0.326558\pi$
$937$	31.7320	1.03664	0.518320	+	0.855187i	$0.326558\pi$
$938$	4.98462	0.162754
$939$	−30.8202	−1.00578
$940$	5.77882	0.188484
$941$	14.7023	0.479281	0.239640	−	0.970862i	$-0.422971\pi$
$941$	14.7023	0.479281	0.239640	+	0.970862i	$0.422971\pi$
$942$	12.9364	0.421491
$943$	−38.1474	−1.24225
$944$	8.75363	0.284906
$945$	2.15386	0.0700652
$946$	−6.33366	−0.205925
$947$	31.6271	1.02774	0.513871	−	0.857867i	$-0.328211\pi$
$947$	31.6271	1.02774	0.513871	+	0.857867i	$0.328211\pi$
$948$	3.45692	0.112276
$949$	4.39676	0.142725
$950$	−1.72826	−0.0560723
$951$	39.4595	1.27956
$952$	1.10111	0.0356871
$953$	−4.94161	−0.160074	−0.0800372	−	0.996792i	$-0.525504\pi$
$953$	−4.94161	−0.160074	−0.0800372	+	0.996792i	$0.525504\pi$
$954$	1.70618	0.0552396
$955$	−20.6161	−0.667121
$956$	−13.4163	−0.433913
$957$	19.7936	0.639835
$958$	−3.79318	−0.122552
$959$	3.57223	0.115353
$960$	−1.58108	−0.0510292
$961$	23.2132	0.748813
$962$	10.6002	0.341764
$963$	0.703109	0.0226574
$964$	−22.0776	−0.711071
$965$	−25.9932	−0.836750
$966$	−3.03423	−0.0976247
$967$	−38.2521	−1.23011	−0.615053	−	0.788486i	$-0.710865\pi$
$967$	−38.2521	−1.23011	−0.615053	+	0.788486i	$0.710865\pi$
$968$	13.5397	0.435184
$969$	−7.73073	−0.248347
$970$	−3.18700	−0.102328
$971$	49.2280	1.57980	0.789901	−	0.613235i	$-0.210132\pi$
$971$	49.2280	1.57980	0.789901	+	0.613235i	$0.210132\pi$
$972$	5.14048	0.164881
$973$	−0.721486	−0.0231298
$974$	26.2840	0.842195
$975$	−2.28470	−0.0731689
$976$	1.75098	0.0560475
$977$	−33.0624	−1.05776	−0.528880	−	0.848697i	$-0.677388\pi$
$977$	−33.0624	−1.05776	−0.528880	+	0.848697i	$0.677388\pi$
$978$	−33.7929	−1.08058
$979$	85.3613	2.72816
$980$	6.84852	0.218768
$981$	4.67865	0.149378
$982$	−1.74390	−0.0556499
$983$	55.4271	1.76785	0.883925	−	0.467628i	$-0.154891\pi$
$983$	55.4271	1.76785	0.883925	+	0.467628i	$0.154891\pi$
$984$	12.2321	0.389944
$985$	−24.3313	−0.775260
$986$	−7.14974	−0.227694
$987$	−3.55605	−0.113190
$988$	2.49738	0.0794522
$989$	−6.30434	−0.200466
$990$	−2.47776	−0.0787482
$991$	49.8570	1.58376	0.791881	−	0.610676i	$-0.209102\pi$
$991$	49.8570	1.58376	0.791881	+	0.610676i	$0.209102\pi$
$992$	−7.36296	−0.233774
$993$	12.7619	0.404986
$994$	1.49505	0.0474200
$995$	−23.6533	−0.749860
$996$	19.9025	0.630635
$997$	−2.18784	−0.0692895	−0.0346448	−	0.999400i	$-0.511030\pi$
$997$	−2.18784	−0.0692895	−0.0346448	+	0.999400i	$0.511030\pi$
$998$	35.9854	1.13910
$999$	40.5961	1.28440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.j.1.9	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.j.1.9	✓	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.58108 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.58108 q^{6} +0.389201 q^{7} +1.00000 q^{8} -0.500177 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.58108 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.58108 q^{6} +0.389201 q^{7} +1.00000 q^{8} -0.500177 q^{9} -1.00000 q^{10} -4.95376 q^{11} +1.58108 q^{12} -1.44502 q^{13} +0.389201 q^{14} -1.58108 q^{15} +1.00000 q^{16} +2.82915 q^{17} -0.500177 q^{18} -1.72826 q^{19} -1.00000 q^{20} +0.615359 q^{21} -4.95376 q^{22} -4.93083 q^{23} +1.58108 q^{24} +1.00000 q^{25} -1.44502 q^{26} -5.53407 q^{27} +0.389201 q^{28} -2.52717 q^{29} -1.58108 q^{30} -7.36296 q^{31} +1.00000 q^{32} -7.83231 q^{33} +2.82915 q^{34} -0.389201 q^{35} -0.500177 q^{36} -7.33567 q^{37} -1.72826 q^{38} -2.28470 q^{39} -1.00000 q^{40} +7.73650 q^{41} +0.615359 q^{42} +1.27856 q^{43} -4.95376 q^{44} +0.500177 q^{45} -4.93083 q^{46} -5.77882 q^{47} +1.58108 q^{48} -6.84852 q^{49} +1.00000 q^{50} +4.47312 q^{51} -1.44502 q^{52} -3.41115 q^{53} -5.53407 q^{54} +4.95376 q^{55} +0.389201 q^{56} -2.73253 q^{57} -2.52717 q^{58} +8.75363 q^{59} -1.58108 q^{60} +1.75098 q^{61} -7.36296 q^{62} -0.194669 q^{63} +1.00000 q^{64} +1.44502 q^{65} -7.83231 q^{66} +12.8073 q^{67} +2.82915 q^{68} -7.79605 q^{69} -0.389201 q^{70} +3.84133 q^{71} -0.500177 q^{72} -3.04269 q^{73} -7.33567 q^{74} +1.58108 q^{75} -1.72826 q^{76} -1.92801 q^{77} -2.28470 q^{78} +2.18643 q^{79} -1.00000 q^{80} -7.24929 q^{81} +7.73650 q^{82} +12.5879 q^{83} +0.615359 q^{84} -2.82915 q^{85} +1.27856 q^{86} -3.99567 q^{87} -4.95376 q^{88} -17.2316 q^{89} +0.500177 q^{90} -0.562403 q^{91} -4.93083 q^{92} -11.6415 q^{93} -5.77882 q^{94} +1.72826 q^{95} +1.58108 q^{96} +3.18700 q^{97} -6.84852 q^{98} +2.47776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} - 2 q^{3} + 12 q^{4} - 12 q^{5} - 2 q^{6} - 9 q^{7} + 12 q^{8}+O(q^{10}) \) 12 * q + 12 * q^2 - 2 * q^3 + 12 * q^4 - 12 * q^5 - 2 * q^6 - 9 * q^7 + 12 * q^8	\( 12 q + 12 q^{2} - 2 q^{3} + 12 q^{4} - 12 q^{5} - 2 q^{6} - 9 q^{7} + 12 q^{8} - 12 q^{10} + q^{11} - 2 q^{12} - 6 q^{13} - 9 q^{14} + 2 q^{15} + 12 q^{16} - 11 q^{17} - 13 q^{19} - 12 q^{20} - 14 q^{21} + q^{22} - 21 q^{23} - 2 q^{24} + 12 q^{25} - 6 q^{26} - 2 q^{27} - 9 q^{28} - 10 q^{29} + 2 q^{30} - 11 q^{31} + 12 q^{32} - 22 q^{33} - 11 q^{34} + 9 q^{35} - 29 q^{37} - 13 q^{38} - 2 q^{39} - 12 q^{40} - q^{41} - 14 q^{42} - 23 q^{43} + q^{44} - 21 q^{46} - 17 q^{47} - 2 q^{48} - 3 q^{49} + 12 q^{50} - 19 q^{51} - 6 q^{52} - 47 q^{53} - 2 q^{54} - q^{55} - 9 q^{56} - 11 q^{57} - 10 q^{58} + 14 q^{59} + 2 q^{60} - 22 q^{61} - 11 q^{62} - 28 q^{63} + 12 q^{64} + 6 q^{65} - 22 q^{66} - 28 q^{67} - 11 q^{68} - q^{69} + 9 q^{70} - 18 q^{71} - 2 q^{73} - 29 q^{74} - 2 q^{75} - 13 q^{76} - 11 q^{77} - 2 q^{78} - 39 q^{79} - 12 q^{80} - 44 q^{81} - q^{82} - 5 q^{83} - 14 q^{84} + 11 q^{85} - 23 q^{86} - 6 q^{87} + q^{88} - 8 q^{89} - 12 q^{91} - 21 q^{92} - 30 q^{93} - 17 q^{94} + 13 q^{95} - 2 q^{96} - 32 q^{97} - 3 q^{98} - 13 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 - 2 * q^3 + 12 * q^4 - 12 * q^5 - 2 * q^6 - 9 * q^7 + 12 * q^8 - 12 * q^10 + q^11 - 2 * q^12 - 6 * q^13 - 9 * q^14 + 2 * q^15 + 12 * q^16 - 11 * q^17 - 13 * q^19 - 12 * q^20 - 14 * q^21 + q^22 - 21 * q^23 - 2 * q^24 + 12 * q^25 - 6 * q^26 - 2 * q^27 - 9 * q^28 - 10 * q^29 + 2 * q^30 - 11 * q^31 + 12 * q^32 - 22 * q^33 - 11 * q^34 + 9 * q^35 - 29 * q^37 - 13 * q^38 - 2 * q^39 - 12 * q^40 - q^41 - 14 * q^42 - 23 * q^43 + q^44 - 21 * q^46 - 17 * q^47 - 2 * q^48 - 3 * q^49 + 12 * q^50 - 19 * q^51 - 6 * q^52 - 47 * q^53 - 2 * q^54 - q^55 - 9 * q^56 - 11 * q^57 - 10 * q^58 + 14 * q^59 + 2 * q^60 - 22 * q^61 - 11 * q^62 - 28 * q^63 + 12 * q^64 + 6 * q^65 - 22 * q^66 - 28 * q^67 - 11 * q^68 - q^69 + 9 * q^70 - 18 * q^71 - 2 * q^73 - 29 * q^74 - 2 * q^75 - 13 * q^76 - 11 * q^77 - 2 * q^78 - 39 * q^79 - 12 * q^80 - 44 * q^81 - q^82 - 5 * q^83 - 14 * q^84 + 11 * q^85 - 23 * q^86 - 6 * q^87 + q^88 - 8 * q^89 - 12 * q^91 - 21 * q^92 - 30 * q^93 - 17 * q^94 + 13 * q^95 - 2 * q^96 - 32 * q^97 - 3 * q^98 - 13 * q^99

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